An efficient algorithm for optimizing whole genome alignment with noise.

Abstract

This paper is concerned with algorithms for aligning two whole genomes so as to identify regions that possibly contain conserved genes. Motivated by existing heuristic-based software tools, we initiate the study of an optimization problem that attempts to uncover conserved genes with a global concern. Another interesting feature in our formulation is the tolerance of noise, which also complicates the optimization problem. A brute-force approach takes time exponential in the noise level. We show how an insight into the optimization structure can lead to a drastic improvement in the time and space requirement [precisely, to O(k2n2) and O(k2n), respectively, where n is the size of the input and k is the noise level]. The reduced space requirement allows us to implement the new algorithm, called MaxMinCluster, on a PC. It is exciting to see that when tested with different real data sets, MaxMinCluster consistently uncovers a high percentage of conserved genes that have been published by GenBank. Its performance is indeed favorably compared to MUMmer (perhaps the most popular software tool for uncovering conserved genes in a whole-genome scale). The source code is available from the website http://www.csis.hku.hk/~colly/maxmincluster/ detailed proof of the propositions can also be found there.